Math Problem Solving Techniques

Which of the following best describes a non-routine problem?

According to Polya's 4-step problem-solving process, which step involves reflecting on the solution and verifying its accuracy?

What is the primary focus during the 'devise a plan' stage of Polya's problem-solving method?

What is the 15th number in the Fibonacci sequence, assuming the sequence starts with 0 and 1?

If a magic square uses numbers 1 to 9, what is the 'magic number' (the sum of each row, column, and diagonal)?

Using the principle of inclusion-exclusion, if 50 students are in a class, 20 take Math, 15 take English, and 5 take both, how many students take neither Math nor English?

In applying problem-solving strategies, which approach is most suitable for proving a mathematical statement for all positive integers?

Mrs. Smith wants to arrange her garden with square flower beds. She has a rectangular space of 12 meters by 18 meters. What is the largest size of square flower bed she can use so that they fit perfectly without any gaps or overlaps, and how many such flower beds can she fit?

Which of the following best describes the role of estimation in the problem-solving process?

A student observes that every multiple of 4 they have encountered is even. They conclude that all multiples of 4 are even. What type of reasoning are they using?

Which of the following is the primary difference between an exercise and a problem, as defined in the content?

A detective uses forensic evidence and witness statements to build a case and identify a suspect in a crime. What type of reasoning is the detective primarily employing?

Given the pattern: 2, 6, 12, 20, 30, __. What is the next number in the sequence, and what type of reasoning is used to determine it?

To solve a word problem, a student decides to first identify the goal, then analyze the obstacles, and finally develop a step-by-step method to overcome those obstacles. Which aspect of problem-solving from the content is the student applying?

A store offers a 25% discount on a refrigerator originally priced at $800 and also waives the sales tax of 8%. What type of problem is this, and how would one solve it?

A researcher formulates a hypothesis that 'exercise improves mood.' They conduct a study, collect data, and analyze the results to determine if the evidence supports their hypothesis. Which type of reasoning are they primarily using?

In a 4x4 magic square using numbers 1 to 16, what is the value of the magic number, which represents the sum of each row, column, and diagonal?

In a survey of 150 factories, how many factories did not purchase any of brands A, B, or C, given the following data: 70 purchased brand A, 75 purchased brand B, 95 purchased brand C, 30 purchased brands A and B, 45 purchased brands A and C, 40 purchased brands B and C, and 10 purchased all three brands?

Mercy's bank account balance at the end of Friday was $451.25. During the day, she wrote a check for $24.50, made an ATM withdrawal of $80, and deposited a check for $235. What was her starting balance at the beginning of the day?

Sofia cuts a 48-inch ribbon into two pieces. One piece is three times as long as the other. What are the lengths of the two pieces?

A factory manufactures three brands of products: A, B, and C. The following data represents the purchasing patterns of 150 factories: 70 bought A, 75 bought B, 95 bought C, 30 bought A and B, 45 bought A and C, 40 bought B and C, and 10 bought all three. How many factories purchased only brand A?

What adjustment should Mercy make to her checkbook balance considering her bank statement shows a deposit of $235, a check written for $24.50, and an ATM withdrawal of $80, and she aims to reconcile her balance to $451.25?

During the process of guess and check method to solve a math problem, what is the most important characteristic of the initial guesses when trying to find two numbers where one is three times the other and their sum is 48?

A magic square contains numbers from 1 to 16, arranged so each row, column, and diagonal sums to the same 'magic number.' Considering this property, if you swap any two numbers within the square, what is the least number of additional swaps necessary to potentially restore the magic square's properties?

In a number guessing game, if initial guesses of 5 and 15 yield a sum less than the target, and 6 and 18 also yield a sum less than the target, what strategy should be employed for the next guess?

Trina's father is 36 years old, and his age is 16 years more than four times Trina's age. Which equation accurately represents this relationship, allowing us to solve for Trina's age ($t$)?

What is the first step in solving a 'work backward' problem?

Consider a two-digit number-guessing game with the following clues: the number is odd, the tens digit is even, the number is prime, and the sum of its digits is 11. What number is described, based on the information?

In the context of recreational math problems, which characteristic is most descriptive?

In the number game where players alternate adding 1 or 2 to the previous number until one reaches 20, what strategy can a player implement to increase their chances of winning, assuming they go first?

Consider a variation of the '20' game where the target number is changed to 30, and players can still only add 1 or 2 to the previous number. If a player announces '26', what number should the next player announce to guarantee a win?

Imagine a sheet of nine stamps arranged in a 3x3 grid. Three stamps must be torn from the sheet such that each stamp is connected to at least one other along an edge. Which of the following configurations is NOT a possible arrangement?

Problem

Exercise

Problem Solving

Problem Solving Process

Inductive Reasoning

Deductive Reasoning

Routine Problem

Problem Example

Non-Routine Problem

Polya's 4-Step Problem Solving

Fibonacci Sequence

Magic Square

Venn Diagrams

Applying Strategies

Comparing Values

Working Backward

Magic Number

Recreational Math Problems

Number Riddle

Guess and Check

Prime Number

Rock-Paper-Scissors

Working Backwards

Problem Solving Strategy

The Number Game

Part-Whole Problem

Stamp Tearing Rules

Guess and Check

Data Graph